Describing Triangles Using Interior Angles

Acute-angled triangles

All the angles in an acute-angled triangle are smaller than 90°.

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Right-angled triangles

The name sort of says it all – right-angled triangles have a right angle in them.  It’s important to remember that since there is only a total of 180° in the interior angles of a triangle, you can’t have more than one right angle inside a triangle.  If you had two right angles, the third angle would have to be zero degrees, and there’s no way you can draw a triangle with one of the angles being zero.

Now because one of the angles in the triangle is a right angle, the other two angles must add up to 90 degrees:


This means that ‘a’ and ‘b’ must each be smaller than 90°.  So the other two angles in a right-angled triangle are acute angles.

Obtuse-angled triangles

Obtuse-angled triangles have one angle in them which is larger than 90°. 

This means that the other two angles in the triangle must together add up to something less than 90 degrees.  So obtuse-angled triangles have one obtuse angle and two acute angles in them.